The Growth of Cities: A Formal Model

23 April 2007 at 9:10 pm Peter G. Klein 1 comment

| Peter Klein |

Luís Bettencourt, José Lobo, Dirk Helbing, Christian Kühnert, and Geoffrey West’s paper “Growth, Innovation, Scaling, and the Pace of Life in Cities” (Proceedings of the National Academy of Sciences 104, no. 17, April 24, 2007) is getting a lot of attention, garnering plugs in Scientific American and Nature. They use data on innovation, employment, wages, GDP, consumption, crime, disease, housing, and infrastructure from US, European, and Chinese cities to estimate a “power law scaling function” linking demographic, socioeconomic, and behavioral indicators to city size. Such indicators, $Y(t),$ are related to population $N(t)$ according to

$Y(t)=Y_0N(t)^{\beta}.$

Findings:

Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, $\beta,$ that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have $\beta \approx 1.2 >1$ (increasing returns), whereas those accounting for infrastructure display $\beta \approx 0.8<1$ (economies of scale). We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which $\beta<1.$ Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse.

For more on cities see these posts on Jane Jacobs and this one on clusters. Here is Ed Glaeser’s influential 1992 paper (with Hedi Kallal, Jose Scheinkman, and Andrei Shleifer) on growth in cities. Other important Glaeser papers on cities include this one with Jesse Shapiro, this one with Albert Saiz, and this one with Christopher Berry. Here is Glaeser’s review of Richard Florida’s Creative Class and here is Florida’s blog. And here is an interesting special issue of the Review of Austrian Economics on the new urbanism.

Update: Here is Florida’s take on the paper.